Probabilistic theories with purification - Quantum Physics

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Abstract: We investigate general probabilistic theories in which every mixed state hasa purification, unique up to reversible channels on the purifying system. Weshow that the purification principle is equivalent to the existence of areversible realization of every physical process, namely that every physicalprocess can be regarded as arising from a reversible interaction of the systemwith an environment, which is eventually discarded. From the purificationprinciple we also construct an isomorphism between transformations andbipartite states that possesses all structural properties of theChoi-Jamiolkowski isomorphism in quantum mechanics. Such an isomorphism allowsone to prove most of the basic features of quantum mechanics, like e.g.existence of pure bipartite states giving perfect correlations in independentexperiments, no information without disturbance, no joint discrimination of allpure states, no cloning, teleportation, no programming, no bit commitment,complementarity between correctable channels and deletion channels,characterization of entanglement-breaking channels as measure-and-preparechannels, and others, without resorting to the mathematical framework ofHilbert spaces.

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